Thorin fought the Easterlings in the Battle of Dale during the War of the Ring, and took refuge in Erebor after his father was killed at its gates, along with Brand king of Dale, so Thorin then became King under the Mountain.
When the news of the Sauron's defeat in the South came to the ears of the enemy, they became dismayed and the Dwarves and Men came forth from the mountain and routed them driving them back of the river Carnen, never troubling them again.
Thorin helped rebuild Erebor and Dale along with Dale's new king Bard II, son of Brand, and once again both their people prospered, and their realms became close allies with the Reunited Kingdom of Arnor and Gondor of King Elessar.

During his rule Gimli, son of Glóin, led a number of Dwarves South to Aglarond, where a new colony was settled. Also during his rule mining for mithril in Moria slowly began again, although Moria was not yet permanently settled.

The origins of the name "Stonehelm" are mysterious: Tolkien doesn't provide us with any account that would shed light on its meaning. The most important historical event that involved Thorin III was the Battle of Dale, so we might speculate that the name is connected to that battle (perhaps even as a reference to his hiding beneath the Lonely Mountain) but no definitive explanation is available.